\[\dfrac{2}{-3} \div \left(-1\dfrac{2}{7}\right) = \]
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We first convert the mixed number $-1\dfrac{2}{7}$ to an improper fraction. Multiplying the denominator 7 by the whole number $-1$ gives $-7$, and adding the numerator 2 gives $-5$. Thus \[-1\dfrac{2}{7} = -\dfrac{5}{7}.\] Therefore, we have \[\dfrac{2}{-3} \div \left(-1\dfrac{2}{7}\right) = \dfrac{2}{-3} \div \left(-\dfrac{5}{7}\right).\]Dividing is the same as multiplying by the reciprocal, so we can rewrite this as \[\dfrac{2}{-3} \cdot \left(-\dfrac{7}{5}\right).\]Multiplying a fraction by $-1$ negates it, so the expression becomes \[-\dfrac{2}{3} \cdot \dfrac{7}{5}.\]Multiplying the numerators gives $(-2)(7) = -14$, and multiplying the denominators gives $(3)(5) = 15$. Therefore, we have \[-\dfrac{2}{3} \cdot \dfrac{7}{5} = \boxed{-\dfrac{14}{15}}.\]
are you sure
I apologize for the previous mistake. Let's correct it:
We start by converting the mixed number $-1\dfrac{2}{7}$ to an improper fraction. We have $-1\dfrac{2}{7} = \dfrac{7(-1) + 2}{7} = \dfrac{-7+2}{7} = \dfrac{-5}{7}$.
Therefore, the expression becomes:
\[\dfrac{2}{-3} \div \left(-1\dfrac{2}{7}\right) = \dfrac{2}{-3} \div \dfrac{-5}{7}\]
Recall that dividing by a fraction is the same as multiplying by its reciprocal. So we can rewrite the expression as:
\[\dfrac{2}{-3} \cdot \dfrac{7}{-5}\]
Multiplying the numerators gives $2\cdot 7 = 14$, and multiplying the denominators gives $-3\cdot -5 = 15$. Thus, the expression simplifies to:
\[\dfrac{2}{-3} \cdot \dfrac{7}{-5} = \dfrac{14}{15}\]
Therefore, $\dfrac{2}{-3} \div \left(-1\dfrac{2}{7}\right) = \boxed{\dfrac{14}{15}}$.
We start by converting the mixed number $-1\dfrac{2}{7}$ to an improper fraction. We have $-1\dfrac{2}{7} = \dfrac{7(-1) + 2}{7} = \dfrac{-7+2}{7} = \dfrac{-5}{7}$.
Therefore, the expression becomes:
\[\dfrac{2}{-3} \div \left(-1\dfrac{2}{7}\right) = \dfrac{2}{-3} \div \dfrac{-5}{7}\]
Recall that dividing by a fraction is the same as multiplying by its reciprocal. So we can rewrite the expression as:
\[\dfrac{2}{-3} \cdot \dfrac{7}{-5}\]
Multiplying the numerators gives $2\cdot 7 = 14$, and multiplying the denominators gives $-3\cdot -5 = 15$. Thus, the expression simplifies to:
\[\dfrac{2}{-3} \cdot \dfrac{7}{-5} = \dfrac{14}{15}\]
Therefore, $\dfrac{2}{-3} \div \left(-1\dfrac{2}{7}\right) = \boxed{\dfrac{14}{15}}$.
are you sure?
Apologies for the confusion.
To compute \[\frac{2}{-3} \div \left(-1\frac{2}{7}\right),\]we can rewrite the mixed number as a fraction by multiplying the whole number part by the denominator and adding the numerator: \[-1\frac{2}{7} = -\frac{7}{7}+\frac{2}{7} = -\frac{7+2}{7} = -\frac{9}{7}.\]Thus, the expression becomes \[\frac{2}{-3} \div \left(-\frac{9}{7}\right).\]We now divide by a fraction by multiplying by the reciprocal: \[\frac{2}{-3} \div \left(-\frac{9}{7}\right) = \frac{2}{-3} \cdot \left(-\frac{7}{9}\right).\]Multiplying the numerators gives $2\cdot7=14$, and multiplying the denominators gives $-3\cdot9=-27$. Therefore, \[\frac{2}{-3} \div \left(-1\frac{2}{7}\right) = \frac{14}{-27} = \boxed{-\frac{14}{27}}.\]
To compute \[\frac{2}{-3} \div \left(-1\frac{2}{7}\right),\]we can rewrite the mixed number as a fraction by multiplying the whole number part by the denominator and adding the numerator: \[-1\frac{2}{7} = -\frac{7}{7}+\frac{2}{7} = -\frac{7+2}{7} = -\frac{9}{7}.\]Thus, the expression becomes \[\frac{2}{-3} \div \left(-\frac{9}{7}\right).\]We now divide by a fraction by multiplying by the reciprocal: \[\frac{2}{-3} \div \left(-\frac{9}{7}\right) = \frac{2}{-3} \cdot \left(-\frac{7}{9}\right).\]Multiplying the numerators gives $2\cdot7=14$, and multiplying the denominators gives $-3\cdot9=-27$. Therefore, \[\frac{2}{-3} \div \left(-1\frac{2}{7}\right) = \frac{14}{-27} = \boxed{-\frac{14}{27}}.\]
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